计算机是否有可能通过用户提供的示例“学习”正则表达式？

You might want to play with this site a bit, it's quite cool and sounds like it does something similar to what you're talking about: http://txt2re.com

I believe the term is "induction". You want to induce a regular grammar.

I don't think it is possible with a finite set of examples (positive or negative). But, if I recall correctly, it can be done if there is an Oracle which can be consulted. (Basically you'd have to let the program ask the user yes/no questions until it was content.)

If its possible for a person to learn a regular expression, then it is fundamentally possible for a program. However, that program will need to be correctly programmed to be able to learn. Luckily this is a fairly finite space of logic, so it wouldn't be as complex as teaching a program to be able to see objects or something like that.

Yes, it's certainly "possible"; Here's the pseudo-code:

string MakeRegexFromExamples(<listOfPosExamples>, <listOfNegExamples>)
{
if HasIntersection(<listOfPosExamples>, <listOfNegExamples>)
return <IntersectionError>


string regex = "";
foreach(string example in <listOfPosExamples>)
{
if(regex != "")
{
regex += "|";
}
regex += DoRegexEscaping(example);
}
regex = "^(" + regex + ")$";


// Ignore <listOfNegExamples>; they're excluded by definition


return regex;
}

The problem is that there are an infinite number of regexs that will match a list of examples. This code provides the simplest/stupidest regex in the set, basically matching anything in the list of positive examples (and nothing else, including any of the negative examples).

I suppose the real challenge would be to find the shortest regex that matches all of the examples, but even then, the user would have to provide very good inputs to make sure the resulting expression was "the right one".

The book An Introduction to Computational Learning Theory contains an algorithm for learning a finite automaton. As every regular language is equivalent to a finite automaton, it is possible to learn some regular expressions by a program. Kearns and Valiant show some cases where it is not possible to learn a finite automaton. A related problem is learning hidden Markov Models, which are probabilistic automata that can describe a character sequence. Note that most modern "regular expressions" used in programming languages are actually stronger than regular languages, and therefore sometimes harder to learn.

@Yuval is correct. You're looking at computational learning theory, or "inductive inference. "

The question is more complicated than you think, as the definition of "learn" is non-trivial. One common definition is that the learner can spit out answers whenever it wants, but eventually, it must either stop spitting out answers, or always spit out the same answer. This assumes an infinite number of inputs, and gives absolutely no garauntee on when the program will reach its decision. Also, you can't tell when it HAS reached its decision because it might still output something different later.

By this definition, I'm pretty sure that regular languages are learnable. By other definitions, not so much...

No computer program will ever be able to generate a meaningful regular expression based solely on a list of valid matches. Let me show you why.

Suppose you provide the examples 111111 and 999999, should the computer generate:

1. A regex matching exactly those two examples: (111111|999999)
2. A regex matching 6 identical digits (\d)\1{5}
3. A regex matching 6 ones and nines [19]{6}
4. A regex matching any 6 digits \d{6}
5. Any of the above three, with word boundaries, e.g. \b\d{6}\b
6. Any of the first three, not preceded or followed by a digit, e.g. (?<!\d)\d{6}(?!\d)

As you can see, there are many ways in which examples can be generalized into a regular expression. The only way for the computer to build a predictable regular expression is to require you to list all possible matches. Then it could generate a search pattern that matches exactly those matches.

If you don't want to list all possible matches, you need a higher-level description. That's exactly what regular expressions are designed to provide. Instead of providing a long list of 6-digit numbers, you simply tell the program to match "any six digits". In regular expression syntax, this becomes \d{6}.

Any method of providing a higher-level description that is as flexible as regular expressions will also be as complex as regular expressions. All tools like RegexBuddy can do is to make it easier to create and test the high-level description. Instead of using the terse regular expression syntax directly, RegexBuddy enables you to use plain English building blocks. But it can't create the high-level description for you, since it can't magically know when it should generalize your examples and when it should not.

It is certainly possible to create a tool that uses sample text along with guidelines provided by the user to generate a regular expression. The hard part in designing such a tool is how does it ask the user for the guiding information that it needs, without making the tool harder to learn than regular expressions themselves, and without restricting the tool to common regex jobs or to simple regular expressions.

There's a language dedicated to problems like this, based on prolog. It's called progol.

As others have mentioned, the basic idea is inductive learning, often called ILP (inductive logic programming) in AI circles.

Second link is the wiki article on ILP, which contains a lot of useful source material if you're interested in learning more about the topic.

I've done some research on Google and CiteSeer and found these techniques/papers:

• Language identification in the limit
• Probably approximately correct learning

Also Dana Angluin's "Learning regular sets from queries and counterexamples" seems promising, but I wasn't able to find a PS or PDF version, only cites and seminar papers.

It seems that this is a tricky problem even on the theoretical level.

Yes, it is possible, we can generate regexes from examples (text -> desired extractions). This is a working online tool which does the job: http://regex.inginf.units.it/

Regex Generator++ online tool generates a regex from provided examples using a GP search algorithm. The GP algorithm is driven by a multiobjective fitness which leads to higher performance and simpler solution structure (Occam's Razor). This tool is a demostrative application by the Machine Lerning Lab, Trieste Univeristy (Università degli studi di Trieste). Please look at the video tutorial here.

This is a research project so you can read about used algorithms here.

Behold! :-)

Finding a meaningful regex/solution from examples is possible if and only if the provided examples describe the problem well. Consider these examples that describe an extraction task, we are looking for particular item codes; the examples are text/extraction pairs:

"The product code is 467-345A" -> "467-345A"
"The item 789-345B is broken"  -> "789-345B"

An (human) guy, looking at the examples, may say: "the item codes are things like \d++-345[AB]"

When the item code is more permissive but we have not provided other examples, we have not proofs to understand the problem well. When applying the human generated solution \d++-345[AB] to the following text, it fails:

"On the back of the item there is a code: 966-347Z"

You have to provide other examples, in order to better describe what is a match and what is not a desired match: --i.e:

"My phone is +39-128-3905 , and the phone product id is 966-347Z" -> "966-347Z"

The phone number is not a product id, this may be an important proof.